Derjaguin, Muller, and Toporov (DMT) – Adhesion theory
March, 25 2025
Table of Contents
Adhesive contact mechanics has become an important area of study in nano- and biosciences. There are various methods developed over the past 75 years to address adhesive interactions in elastic contact problems. The emphasis is on connecting the local physical mechanisms of adhesion with macroscopic mechanical loading, with particular attention given to the contact equations. Adhesive contacts are crucial in various technological fields. Efficient manufacturing processes, like wafer cleaning in semiconductor technology, require tight control over surface contamination. Energy-efficient mechanical devices and reliable micromechanical systems depend on better management of friction and lubrication. Understanding key phenomena, such as particle immobilization or release in filtration, controlled positioning in reproduction devices, and the settling of bioorganisms on surfaces in health and biotechnology, is essential for further advancements.
The Derjaguin, Muller, and Toporov (DMT) adhesion theory applies to elastic contact with adhesion between two locally spherical bodies under a normal force, without friction. It builds on the Hertz theory of contact but incorporates adhesion by assuming that the Hertz deformation profile remains unchanged by adhesion. The DMT theory is suitable for small values of the Tabor parameter, which corresponds to small radii, low adhesion, and high modulus materials. The DMT theory can also be applied to the adhesive contact of two elastically deformable spherical particles. It is generally considered suitable for small particles that have a high elastic modulus and low work of adhesion.
Figure-1 The geometry of the DMT adhesive contact involves attractive interactions that act over the cohesive zone, which is an annulus with radius c surrounding the contact zone with radius a. The DMT model applies if c is greater than a.
The pull-out force for the DMT theory is
Fpullout = -2 πRw Where w is the adhesion energy and R is the contact radius
As these more general results demonstrate, the DMT model depends on the interaction potential and the punch shape. Unlike the Derjaguin 1934 model, which assumes the pull-out force is controlled by the creation or destruction of the contact area, the DMT model suggests that the pull-out force is influenced by the motion of the punch in the long-range interaction potential. In this model, the adhesion energy w (which is coupled to the contact area) is not the relevant concept. Instead, the key parameter for adhesion is the amplitude of the interaction potential V₀. In the DMT theory, the punch displacement directly couples to the interaction potential.
Figure-2 The schematic illustration shows the formation of a neck at the contact edge. In a thought experiment, an adhesionless contact is initially formed. When adhesion is introduced, the contact area begins to spread out (a). If a (negative) flat punch displacement is applied, it restrains the growth of the contact area, preserving the contact radius (b).
I am a postgraduate researcher at the University of Leeds. I have completed my master's degree in the Erasmus Tribos program at the University of Leeds, University of Ljubljana, and University of Coimbra and my bachelor's degree in Mechanical Engineering from VTU in NMIT, India. I am an editor and social networking manager at TriboNet. I have a YouTube channel called Tribo Geek where I upload videos on travel, research life, and topics for master's and PhD students.
